On Optimal Jamming in Strategic Communication

Abstract

This paper studies the well-known jamming problems in the context of strategic communication, a variation of the Bayesian Persuasion problem information economics. A communication problem with three agents, a transmitter, a receiver and a jammer, is considered. All players have diverging objectives: the transmitter and the receiver want to minimize their individual distortion functions while the jammer aims to maximize a convex combination of these functions. This leads to a hierarchical game whose equilibrium solutions are studied here. Here, the transmitter is the leader and hence announces an encoding strategy with full commitment, where the receiver acts as the follower. The game between the jammer and the transmitter-the receiver pair depends on the ability of this communicating pair to secretly agree on a random event, that is “common randomness”. In the presence of common randomness, the problem becomes a zero-sum game for which a saddle-point solution is sought. The saddle-point solution consists of randomized linear strategies for the communicating pair and additive independent Gaussian noise for the jammer. If common randomness is not available, then this problem does not admit a saddle-point solution. We derive and analyze the Stackelberg equilibrium between the communicating pair and the jammer, and show that equilibrium achieving strategies for all agents are linear/affine.